\[ \int x^{-m} (-a-b x)^{-n} (a+b x)^n \, dx \]
Optimal antiderivative \[ \frac {x^{1-m} \left (b x +a \right )^{n} \left (-b x -a \right )^{-n}}{1-m} \]
command
integrate((b*x+a)**n/(x**m)/((-b*x-a)**n),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {x \left (a + b x\right )^{n}}{m x^{m} \left (- a - b x\right )^{n} - x^{m} \left (- a - b x\right )^{n}} & \text {for}\: m \neq 1 \\\begin {cases} e^{- i \pi n} \log {\left (-1 + \frac {b \left (\frac {a}{b} + x\right )}{a} \right )} & \text {for}\: \left |{\frac {b \left (\frac {a}{b} + x\right )}{a}}\right | > 1 \\e^{- i \pi n} \log {\left (1 - \frac {b \left (\frac {a}{b} + x\right )}{a} \right )} & \text {otherwise} \end {cases} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________